Analyses of Bulk and Surface Acoustic Waves in 2D Phononic Crystal Waveguides Using FDTD Method
Date Issued
2006
Date
2006
Author(s)
Sun, Jia-Hong
DOI
en-US
Abstract
Phononic crystal research covers both of the fields of solid-state physics and elastodynamic theory. A phononic crystal is constructed of multi-types elastic materials arranged periodically in space, and acoustic waves propagating in it is affected by the periodic scatters. A specific property is band gaps resulted from the discontinuity of eigenmodes, and thus propagation of acoustic waves is forbidden in this frequency range. This property inspires the attempts to control acoustic waves and develop the acoustic circuit engineering. In this text, one of the important components – phononic crystal waveguide is analyzed and the techniques of manipulating waves in the waveguides are discussed.
In this thesis, the finite-difference time-domain (FDTD) method is adopted. FDTD method is a flexible tool and widely used in the study of wave propagations. In this study, the difference equations are derived and the necessary boundary conditions, i.e., Bloch’s periodic condition and perfectly matched layer (PML), are introduced. With these conditions, the FDTD can not only calculate the transient wave propagation but also analyze the dispersion of the periodic structures. Besides, analyzing surface waves consumes huge computation power, and therefore a PC Cluster system is established to serve parallel calculation. A parallel FDTD program is realized with message passing interface (MPI) library. With the PC cluster and parallel calculation, study of surface waves inside waveguides is accelerated and becomes feasible.
The technique of analyzing dispersions of phononic crystals using FDTD method is presented firstly. The properties of steel/epoxy, tungsten/silicon and AlAs/GaAs phononic crystals are calculated. The eigenmodes of both BAW and SAW are calculated and complete band gaps are obtained in the steel/epoxy and tungsten/silicon cases. Based on the complete band gaps, phononic crystal waveguides are designed by connecting point defects in phononic crystals. To investigate the defect modes inside the waveguides, the supercell technique is used and the dispersion relations of bulk and surface waves are obtained. The guided waves inside waveguides are investigated and the propagation is demonstrated. Further, the effect of coupling waveguides and the waveguide width is discussed. Then a waveguide coupler is designed to select the wave of a specific wavelength in a dual waveguides system. Besides, an improved bending waveguide is reported to improve the transmission of surface waves. To sum up, a procedure of analyzing phononic crystals and designing waveguides has been presented in this work and the results can serve as an important foundation for the future development of acoustic circuits.
Subjects
聲子晶體
時間域有限差分法
波導
phononic crystals
finite-difference time-domain method
waveguides
Type
thesis
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